Find the indefinite integral z 2 x 3 10 x 2 11 x 7 x

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Question 3.[5 points] Find the indefinite integralZ2x3-10x2+ 11x+ 7x2-5x+ 6dx.
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Question 4.[4 points] For the following improper integral, determine whether it converges,and determine its value if it does.Z332 + 4x2dx
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Question 5.[5 points] Consider the functionsf(x) =1xandg(x) =x2, forx >0.Find the area enclosed between the graphs off,gand the linex= 2. Hint: First find thepoints of intersection of the graphs offandg.2as follows:x3= 1 = 13, hencex= 1.
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Question 6.[6 points] Zombies have invaded campus! They recruit more of the undead atrate:dzdt=f(z) =z-5z2+ 4z3,wheretis time andzis the number of zombies (in thousands).a) Determine all biologically meaningful steady states (equilibrium points) of this dynamicalsystem.b)Determine the stability of each steady state in (a), using the derivative test.c)Draw a phase-line diagram.d)If two zombies are on campus initially, how many will there be eventually?

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